create random distribution of dupli objects on particle system but keeping one object per face
I noticed that you haven't changed the random slider (the one next to the 'object' slider, at the top of the particle settings). For the rest of the random settings to work, you need to make this a non-zero value. This only controls the distribution, rather than the rotation, so you shouldn't have any worries on that score.

This might not solve your one object per face issue, however. Perhaps try applying your group particle system to a plane the size of one of those faces and using an array modifier. This should achieve the intended result.